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24 posts tagged geometry
Prove πR² using only beads and a ruler! via Minutephysics.
Metric-Aware Processing of Spherical Imagery
The adapted grid hierarchy is regularly spaced along meridians but adaptively spaced across circles of latitude. The multiresolution refinement (left-to-right) supports a set of nested finite elements, which enable an efficient, metric-aware multigrid solver.
(Source, Computer Graphics Group -Department of Computer Science- at Johns Hopkins University)
A right-angled spherical triangle.
arc AB + arc BC = arc AC
Source: Wikimedia Commons, File: Spherical triangle.svg
![Ilmanen’s “Planosphere” (~1994 & 2010). Complete, embedded of genus g. One non-compact end, asymptotic to a regular cone w/ 4g+g symmetries.
Ref.: [1] T. Ilmanen. Lectures on Mean Curvature Flow and Related Equations, Conference on Partial Differential Equations & Applications to Geometry, 1995, ICTP, Trieste. [2] N. Kapouleas, S. Kleene, N.M. Møller. Mean curvature self-shrinkers of high genus: Non-compact examples. [Rigorous proof of existence/construction via gluing. Link: arxiv:1106.5454]
Source: Embedded Mean Curvature Self-shrinkers in R^3, Niels Martin Møller, Department of Mathematics at MIT](http://24.media.tumblr.com/tumblr_lvsn02uAny1qaityko1_1280.jpg)
Ilmanen’s “Planosphere” (~1994 & 2010). Complete, embedded of genus g. One non-compact end, asymptotic to a regular cone w/ 4g+g symmetries.
Ref.: [1] T. Ilmanen. Lectures on Mean Curvature Flow and Related Equations, Conference on Partial Differential Equations & Applications to Geometry, 1995, ICTP, Trieste. [2] N. Kapouleas, S. Kleene, N.M. Møller. Mean curvature self-shrinkers of high genus: Non-compact examples. [Rigorous proof of existence/construction via gluing. Link: arxiv:1106.5454]
Source: Embedded Mean Curvature Self-shrinkers in R^3, Niels Martin Møller, Department of Mathematics at MIT
Dew Drops on a spider web are spherical, until they become too large and become deformed by gravity.
Source: Patterns of Nature, Exploratorium
Flotilla is a video of micro-origamis (2 ou 3 centimeters long) which are opening slowly onto the surface of the water by capillarity.
Credit: Etienne Cliquet
(Absolutely stunning, don’t you dare miss it!)